Modifying a hierarchical representation of a circuit to process composite gates

ABSTRACT

One embodiment of the invention provides a system for analyzing a layout related to a circuit on a semiconductor chip. The system operates by receiving a design hierarchy specifying the layout of the circuit. This design hierarchy includes a set of hierarchically organized nodes, wherein a given node in the design hierarchy specifies a geometrical feature that is comprised of lower-level geometrical features that are represented by lower-level nodes located under the given node in the design hierarchy. The system modifies the design hierarchy by, examining a set of sibling nodes that are located under a parent node in the design hierarchy in order to identify a set of interacting geometrical features between the set of sibling nodes. The system then moves the set of interacting geometrical features from the sibling nodes to the parent node, so that the interaction is visible at the parent node. Note that other geometrical features that do not interact remain at the sibling nodes and are not moved to the parent node. The system then performs an analysis on the modified design hierarchy. This involves analyzing the set of interacting geometrical features at the parent node.

RELATED APPLICATION

[0001] The subject matter of this application is related to the subject matter in a co-pending non-provisional application by the same inventor as the instant application and filed on the same day as the instant application entitled, “Modifying a Hierarchical Representation of a Circuit to Process Features Created by Interactions Between Cells,” having serial number TO BE ASSIGNED, and filing date TO BE ASSIGNED (Attorney Docket No. NTMC-0734).

BACKGROUND

[0002] 1. Field of the Invention

[0003] The invention relates to the process of designing an integrated circuit. More specifically, the invention relates to a method and an apparatus for modifying a hierarchical representation of a circuit in order to efficiently analyze features created by interactions between cells in the hierarchical representation.

[0004] 2. Related Art

[0005] Recent advances in integrated circuit technology have largely been accomplished by decreasing the feature size of circuit elements on a semiconductor chip. As the feature size of these circuit elements continues to decrease, circuit designers are forced to deal with problems that arise as a consequence of the optical lithography process that is typically used to manufacture integrated circuits. This optical lithography process generally begins with the formation of a photoresist layer on the surface of a semiconductor wafer. A mask composed of opaque regions, which are generally formed of chrome, and light-transmissive clear regions, which are generally formed of quartz, is then positioned over this photo resist layer coated wafer. (Note that the term “mask” as used in this specification is meant to include the term “reticle.”) Exposure energy is then shone on the mask from an exposure energy source, such as a visible light source or an ultraviolet light source.

[0006] This exposure energy is generally reduced and focused through an optical system that contains a number of lenses, filters and mirrors. The exposure energy passes through the clear regions of the mask and exposes the underlying photoresist layer. At the same time, the exposure energy is blocked by opaque regions of mask, leaving underlying portions of the photoresist layer unexposed.

[0007] The exposed photoresist layer is then developed, typically through chemical removal of the exposed/non-exposed regions of the photoresist layer. The end result is a semiconductor wafer with a photoresist layer having a desired pattern. This pattern can then be used for etching underlying regions of the wafer.

[0008] A layout for a semiconductor chip is often stored in a standard hierarchical format, such as GDSII stream format. For example, FIGS. 1A, 1B and 1C illustrate how a layout, T, can be composed of a sub-cell A and a sub-cell B, wherein the sub-cell A further includes a sub-cell C. FIG. 1A illustrates a nodal representation of this hierarchy, while FIG. 1B illustrates a corresponding graphical representation.

[0009]FIG. 1C presents a specification of the layout in code form. In this form, the layout, T, includes a reference list. This reference list includes a reference to cell A along with an associated transformation, T_(A), and a reference to cell B along with an associated transformation, T_(R). Similarly, the layout for cell A includes geometrical features associated with cell A along with a reference cell C. This reference to cell C is accompanied by a transformation of cell C with respect to A, T_(CA). The layouts for cell B and cell C include geometrical features associated with cell B and cell C, respectively.

[0010] Representing a layout in a hierarchical form can cause problems for various operations related to fabrication of a semiconductor chip, because interactions between nodes within the hierarchical representation can cause unintended results. These problems can be remedied by collapsing the hierarchy down into a single monolithic layout before performing the operations. Unfortunately, this can be prohibitively slow because the operations must be applied to the entire monolithic layout, even though many of the cells in the layout may be repeated.

[0011] What is needed is a method and an apparatus for performing a computational operation on a hierarchical representation of a layout without performing the computational operation over the entire layout, and without the above-described problems associated with using a hierarchical representation.

[0012] In particular, one problem arises during the generation of phase shifters. Phase shifters are often incorporated into a mask in order to achieve line widths that are smaller than the wavelength of the exposure energy that is used to expose the photoresist layer through the mask. During phase shifting, the destructive interference caused by two adjacent clear areas on a mask is used to create an unexposed area on the photoresist layer. This is accomplished by exploiting the fact that exposure energy passing through a mask's clear regions exhibits a wave characteristic having a phase that is a function of the distance the exposure energy travels through the mask material. By placing two clear areas adjacent to each other on the mask, one of thickness t₁ and the other of thickness t₂, one can obtain a desired unexposed area on the underlying photoresist layer caused by interference. By varying the thickness t₁ and t₂ appropriately, the exposure energy exiting the material of thickness t₂ is 180 degrees out of phase with the exposure energy exiting the material of thickness t₁. Phase shifting is described in more detail in U.S. Pat. No. 5,858,580, entitled “Phase Shifting Circuit Manufacture Method and Apparatus,” by inventors Yao-Ting Wang and Yagyensh C. Pati, filed Sep. 17, 1997 and issued Jan. 12, 1999, which is hereby incorporated by reference.

[0013] For example, referring to FIG. 2A, a phase shifter is composed of a zero degree phase clear area 254 that works in concert with a 180-degree phase clear area 258 to reduce the width of polysilicon line 256 in the gate region of a transistor 250. This first transistor selectively creates a conducting path between diffusion region 252 and diffusion region 260.

[0014] Note that a thin chromium regulator 255 can be added to the mask between zero-degree phase clear area 254 and 180-degree phase clear area 258 in order to better control gate width.

[0015] The phase shifter is typically incorporated into a separate phase shifting mask, which is used to reduce the width of polysilicon line 256 in the gate region of transistor 250.

[0016] Phase shifters are typically extended past the active diffusion region of a transistor by a certain margin. For example, in FIG. 2B, the phase shifter comprised of the zero-degree phase region 204 and 180-degree phase region 206 is extended past the endcap of the transistor by an endcap margin 212 (for example, 200 nm). On the other side of the transistor, the phase shifter is extended past the active diffusion region by a fieldcap margin 214 (for example, 80 nm). Note that the endcap margin 212 is larger than the fieldcap margin 214 because the transistor endcap may be susceptible to line end shortening, which can be somewhat mitigated by extending the phase shifter by an additional margin.

[0017] Sizing phase shifters can be a problem in a hierarchical layout because interactions between cells may case endcaps to become fieldcaps. For example in FIG. 3A, endcap 306 in cell 302 joins with endcap 316 in cell 304 so that they are no longer endcaps. Similarly, in FIG. 3B, endcap 306 in cell 302 interacts with polysilicon region 322 in cell 320 to form a fieldcap. In both of these examples, it is desirable to know that the inter-cell interactions cause endcaps 306 and 316 to become fieldcaps in order to appropriately size the phase shifters. However, using existing techniques, this can only be accomplished by collapsing the design hierarchy so that the interactions become visible. As mentioned above, collapsing the design hierarchy can greatly increase the time required to process the layout.

[0018] Hence, what is needed is a method and an apparatus for forming phase shifters using a hierarchical representation of a layout without unnecessarily collapsing the layout.

SUMMARY

[0019] One embodiment of the invention provides a system for analyzing a layout related to a circuit on a semiconductor chip. The system operates by receiving a design hierarchy specifying the layout of the circuit. This layout includes a set of hierarchically organized nodes, wherein a given node specifies a geometrical feature that is comprised of lower-level geometrical features that are represented by lower-level nodes located under the given node in the design hierarchy. The system operates by modifying the design hierarchy by examining a set of sibling nodes that are located under a parent node in the design hierarchy in order to identify a set of interacting geometrical features between the set of sibling nodes. Next, the system then moves the set of interacting geometrical features to a new child node under the parent node, and then performs an analysis on the modified design hierarchy.

[0020] In one embodiment of the invention, the system identifies other sets of sibling nodes with equivalent sets of interacting geometrical features. This allows the system to use the new child node in analyzing the other sets of sibling nodes, so that additional child nodes do not have to be recreated for the other sets of sibling nodes.

[0021] In one embodiment of the invention, while moving the set of interacting geometrical features to the new child node, the system first moves the set of interacting geometrical features from the set of sibling nodes to the parent node. Next, the system creates the new child node under the parent node, and then moves the set of interacting geometrical features from the parent node to the new child node.

[0022] In one embodiment of the invention, the system also identifies a second set of interacting geometrical features between the parent node and the set of sibling nodes. The system then moves this second set of interacting geometrical features from the parent node to the set of sibling nodes.

[0023] In one embodiment of the invention, performing the analysis involves identifying transistors and associated transistor endcaps within the circuit, wherein the set of interacting geometrical features defines at least some of the transistors and associated transistor endcaps. Next, the system generates phase shifters to be used in fabricating some of the identified transistors, wherein the layout of a given phase shifter is affected by a location of an associated endcap for the given phase shifter.

[0024] In one embodiment of the invention, the set of interacting geometrical features define diffusion regions on the semiconductor chip.

[0025] In one embodiment of the invention, the layout can define either features on the semiconductor chip, or a mask that is used to create features on the semiconductor chip.

[0026] In one embodiment of the invention, the design hierarchy is specified in GDSII format.

[0027] One embodiment of the invention provides a system for analyzing a layout related to a circuit on a semiconductor chip. The system operates by receiving a design hierarchy specifying the layout of the circuit. This design hierarchy includes a set of hierarchically organized nodes, wherein a given node in the design hierarchy specifies a geometrical feature that is comprised of lower-level geometrical features that are represented by lower-level nodes located under the given node in the design hierarchy. The system modifies the design hierarchy by, examining a set of sibling nodes that are located under a parent node in the design hierarchy in order to identify a set of interacting geometrical features between the set of sibling nodes. The system then moves the set of interacting geometrical features from the sibling nodes to the parent node, so that the interaction is visible at the parent node. Note that other geometrical features that do not interact remain at the sibling nodes and are not moved to the parent node. The system then performs an analysis on the modified design hierarchy. This involves analyzing the set of interacting geometrical features at the parent node.

[0028] In one embodiment of the invention, the system determines at a parent node whether interactions between related sibling nodes cause transistor endcaps to become fieldcaps, and if so, moves geometrical features that caused the interactions to the parent node.

[0029] In one embodiment of the invention, the set of interacting geometrical features define polysilicon regions and diffusion regions on the semiconductor chip.

BRIEF DESCRIPTION OF THE FIGURES

[0030]FIG. 1A illustrates a hierarchical representation of a layout in nodal form.

[0031]FIG. 1B illustrates a hierarchical representation of the layout in graphical form.

[0032]FIG. 1C illustrates a hierarchical representation of the layout in code form.

[0033]FIG. 2A illustrates a phase shifter used to form a transistor.

[0034]FIG. 2B illustrates endcap and fieldcap margins for a phase shifter.

[0035]FIG. 3A illustrates an interaction between transistor endcaps in different cells.

[0036]FIG. 3B illustrates an interaction between a transistor endcap and a polysilicon line from different cells.

[0037]FIG. 4 illustrates the processing of a hierarchical layout in accordance with an embodiment of the invention.

[0038]FIG. 5A presents a flow chart illustrating the “push diffusion” process in accordance with an embodiment of the invention.

[0039]FIG. 5B illustrates and exemplary hierarchical layout in accordance with an embodiment of the invention.

[0040]FIG. 6 presents a flow chart illustrating the processing of a composite gate in accordance with an embodiment of the invention.

[0041]FIG. 7 illustrates an exemplary hierarchical layout in accordance with an embodiment of the invention.

DETAILED DESCRIPTION

[0042] Layout Processing

[0043]FIG. 4 illustrates the processing of a hierarchical layout in accordance with an embodiment of the invention. The system starts with an input layout 402 in a hierarchical format, such as GDSII stream format. Next, the system performs a preprocessing operation 404, which modifies cells in input layout 402 in order to improve the efficiency of subsequent processing operations. For example, the system may collapse small cells that contain too few geometrical features (shapes) into other cells. This reduces the inefficiency of having to process too many small cells. The system may also merge cells that have too many overlapping geometrical features.

[0044] Next, the system performs “push diffusion” processing 406. This operation can move features that specify diffusion regions down to child nodes that have interacting polys with diffusion regions from parent or other sibling nodes, and can thereby create new gates at the child nodes. This process is described in more detail below with reference to FIG. 5.

[0045] The next process involves performing “composite gate” processing 408 to move to the common parent the interacting gates from child nodes. This composite gate processing is described in more detail below with reference to FIG. 6.

[0046] Note that some embodiments of the present invention perform only push diffusion processing 406 and not composite gate processing 408, while other embodiments perform only composite gate processing 408 and not push diffusion processing 406. Yet other embodiments perform both push diffusion processing 406 and composite gate processing 408.

[0047] Next, the system performs a shifter placement operation 410 to place phase shifters over identified transistors. Note that these phase shifters are sized based upon the existence of endcaps and fieldcaps on the transistors. The system also performs a design rule checking operation 412 to ensure that the shifter placement does not violate design rules. Note that the system may additionally iterate the shifter placement operation 410 and the design rule checking operation 412 in order to satisfy the design rules.

[0048] The system also performs a coloring operation 414 on the phase shifters to ensure that the phase shifters do not violate coloring constraints. During the coloring operation 414, the zero-degree phase regions and the 180-degree phase regions of the shifters are colored with different colors. The system then checks for unintended interactions between differently colored regions in order to prevent unintended side effects during the phase shifting process.

[0049] After the coloring operation 414, the system produces output layout 416, which includes phase shifters used to produce the circuit.

[0050] Push Diffusion Process

[0051]FIG. 5A presents a flow chart illustrating the push diffusion process in accordance with an embodiment of the invention. The system starts by receiving a design hierarchy that specifies the circuit layout (step 502).

[0052] Next, the system performs the following operations for each parent node and associated child node in the design hierarchy. The system first identifies interacting diffusion and poly geometries (step 504). These interactions can take place between child (sibling) nodes or between the parent node and the child nodes. For example, in FIG. 5B, the system finds interaction regions between child nodes A and B, as well as interactions between parent node T and child nodes A and B. Next, the system moves the diffusion geometries within these interacting regions to the parent node T (step 506). In one embodiment of the present invention, these interacting features define diffusion regions in the circuit.

[0053] Next, the system identifies the child cells that have poly geometries that interact with these diffusion geometries, and creates a new clone copy of child node, A′, (step 508) and then moves the interacting geometrical features to the new child node, A′ (step 510).

[0054] Note that during the above-described process features that do not interact remain at child nodes, A and B, and parent node, T. Also note that diffusion geometries within child nodes that interact with poly geometries within parent nodes are moved to the parent nodes.

[0055] The process also identifies identical geometries that are being moved to different instances of the same cell in order to minimize numbers of the clones created for the cell.

[0056] Composite Gate Processing

[0057]FIG. 6 presents a flow chart illustrating the processing of a composite gate in accordance with an embodiment of the invention. The system starts by receiving a design hierarchy that specifies the circuit layout (step 602).

[0058] The system first identifies interacting geometrical features (step 604). These interactions can take place between child (sibling) nodes or between the parent node and the child node. For example, in FIG. 7, the system finds interactions between child nodes A 706 and B 707 and between parent node G 703 and child nodes A 706 and B 707. Next, the system moves the interacting features to the parent node G 703 (step 606).

[0059] If an equivalent set of interacting features occur again in the design hierarchy, the system does not redo the analysis, but instead uses the analysis that has already been done for the interacting geometrical features (step 608). For example referring to FIG. 8, if the same interacting geometrical features occur under parent node T 802 between sibling nodes A 808 and B 809, the system does note redo the analysis on the interacting features for nodes A 808 and B 809, but instead reuses the analysis for nodes A 806 and B 807.

[0060] Note that the system determines if a set of interacting features are equivalent by determining if they have the same cells interacting with the same relative transformation with respect to each other. In this case, the region of interaction can be duplicated.

[0061] Next, the system detects transistors and associated endcaps for node H 704 (step 610). This can involve determining at cell T 702 whether an endcap in a cell G 703 interacts with other endcaps or polysilicon features in cell H 704 or in cell I 705. If any endcaps are changed through interactions with other cells, the system moves the interacting shapes and their associated gates to the parent node T 702 (step 612). Note that the other features that are not involved in the interaction remain located at the child nodes G 703, H 704 and I 705.

[0062] At this point, after diffusion processing 406 and composite gate processing 408 have occurred (see FIG. 4), shifter placement 410 can be performed on the modified design hierarchy, wherein diffusion layers are in child nodes and geometries are in parent nodes.

[0063] The data structures and code described in this detailed description are typically stored on a computer readable storage medium, which may be any device or medium that can store code and/or data for use by a computer system. This includes, but is not limited to, magnetic and optical storage devices such as disk drives, magnetic tape, CDs (compact discs) and DVDs (digital versatile discs or digital video discs), and computer instruction signals embodied in a transmission medium (with or without a carrier wave upon which the signals are modulated). For example, the transmission medium may include a communications network, such as the Internet.

[0064] The preceding description is presented to enable any person skilled in the art to make and use the invention, and is provided in the context of a particular application and its requirements. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the invention. Thus, the above disclosure is not intended to limit the invention. The scope of the invention is defined by the appended claims. 

What is claimed is:
 1. A method for analyzing a layout related to a circuit on a semiconductor chip, comprising: receiving a design hierarchy specifying the layout of the circuit, including a set of hierarchically-organized nodes; wherein a given node in the design hierarchy specifies a geometrical feature that is comprised of lower-level geometrical features that are represented by lower-level nodes located under the given node in the design hierarchy; modifying the design hierarchy to produce a modified design hierarchy by, examining a set of sibling nodes that are located under a parent node in the design hierarchy, identifying a set of interacting geometrical features between the set of sibling nodes, and moving the set of interacting geometrical features from the sibling nodes to the parent node, so that the interaction is visible at the parent node, wherein other geometrical features that do not interact remain at the sibling nodes and are not moved to the parent node; and performing an analysis on the modified design hierarchy; wherein performing the analysis involves analyzing the set of interacting geometrical features at the parent node.
 2. The method of claim 1, further comprising: identifying other sets of sibling nodes with equivalent sets of interacting geometrical features; and using results from analyzing the set of interacting geometrical features in analyzing the equivalent sets of interacting geometrical features, so that the analysis does not have to be repeated for the equivalent sets of interacting geometrical features.
 3. The method of claim 1, wherein performing the analysis involves: identifying transistors and associated transistor endcaps within the circuit; wherein the set of interacting geometrical features defines at least some of the transistors and associated transistor endcaps; and generating phase shifters to be used in fabricating some of the identified transistors; wherein the layout of a given phase shifter is affected by a location of an associated endcap for the given phase shifter.
 4. The method of claim 3, further comprising determining at a parent node whether interactions between related sibling nodes cause transistor endcaps to become fieldcaps, and if so, moving geometrical features that caused the interactions to the parent node.
 5. The method of claim 1, wherein modifying the design hierarchy additionally involves: identifying a second set of interacting geometrical features between the parent node and the set of sibling nodes; and moving the second set of interacting geometrical features from the set of sibling nodes to the parent node.
 6. The method of claim 1, wherein the set of interacting geometrical features define polysilicon regions and diffusion regions on the semiconductor chip.
 7. The method of claim 1, wherein the layout can define: features on the semiconductor chip; and a mask that is used to create features on the semiconductor chip.
 8. The method of claim 1, wherein the design hierarchy is specified in GDSII format.
 9. A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for analyzing a layout related to a circuit on a semiconductor chip, the method comprising: receiving a design hierarchy specifying the layout of the circuit, including a set of hierarchically-organized nodes; wherein a given node in the design hierarchy specifies a geometrical feature that is comprised of lower-level geometrical features that are represented by lower-level nodes located under the given node in the design hierarchy; modifying the design hierarchy to produce a modified design hierarchy by, examining a set of sibling nodes that are located under a parent node in the design hierarchy, identifying a set of interacting geometrical features between the set of sibling nodes, and moving the set of interacting geometrical features from the sibling nodes to the parent node, so that the interaction is visible at the parent node, wherein other geometrical features that do not interact remain at the sibling nodes and are not moved to the parent node; and performing an analysis on the modified design hierarchy; wherein performing the analysis involves analyzing the set of interacting geometrical features at the parent node.
 10. The computer-readable storage medium of claim 9, wherein the method further comprises: identifying other sets of sibling nodes with equivalent sets of interacting geometrical features; and using results from analyzing the set of interacting geometrical features in analyzing the equivalent sets of interacting geometrical features, so that the analysis does not have to be repeated for the equivalent sets of interacting geometrical features.
 11. The computer-readable storage medium of claim 9, wherein performing the analysis involves: identifying transistors and associated transistor endcaps within the circuit; wherein the set of interacting geometrical features defines at least some of the transistors and associated transistor endcaps; and generating phase shifters to be used in fabricating some of the identified transistors; wherein the layout of a given phase shifter is affected by a location of an associated endcap for the given phase shifter.
 12. The computer-readable storage medium of claim 11, wherein the method further comprises, determining at a parent node whether interactions between related sibling nodes cause transistor endcaps to become fieldcaps, and if so, moving geometrical features that caused the interactions to the parent node.
 13. The computer-readable storage medium of claim 9, wherein modifying the design hierarchy additionally involves: identifying a second set of interacting geometrical features between the parent node and the set of sibling nodes; and moving the second set of interacting geometrical features from the set of sibling nodes to the parent node.
 14. The computer-readable storage medium of claim 9, wherein the set of interacting geometrical features define polysilicon regions and diffusion regions on the semiconductor chip.
 15. The computer-readable storage medium of claim 9, wherein the layout can define: features on the semiconductor chip; and a mask that is used to create features on the semiconductor chip.
 16. The computer-readable storage medium of claim 9, wherein the design hierarchy is specified in GDSII format.
 17. An apparatus for analyzing a layout related to a circuit on a semiconductor chip, comprising: a receiving mechanism that is configured to receive a design hierarchy specifying the layout of the circuit, including a set of hierarchically-organized nodes; wherein a given node in the design hierarchy specifies a geometrical feature that is comprised of lower-level geometrical features that are represented by lower-level nodes located under the given node in the design hierarchy; a modification mechanism that is configured to modify the design hierarchy to produce a modified design hierarchy; wherein the modification mechanism is configured to, identify a set of interacting geometrical features between a set of sibling nodes that are located under a parent node in the design hierarchy, and to move the set of interacting geometrical features from the sibling nodes to the parent node, so that the interaction is visible at the parent node, wherein other geometrical features that do not interact remain at the sibling nodes and are not moved to the parent node; and an analysis mechanism that is configured to perform an analysis on the modified design hierarchy; wherein performing the analysis involves analyzing the set of interacting geometrical features at the parent node.
 18. The apparatus of claim 17, further comprising: an identification mechanism that is configured to identify other sets of sibling nodes with equivalent sets of interacting geometrical features; and wherein the analysis mechanism is configured to use results from analyzing the set of interacting geometrical features in analyzing the equivalent sets of interacting geometrical features, so that the analysis does not have to be repeated for the equivalent sets of interacting geometrical features.
 19. The apparatus of claim 17, wherein the modification mechanism is additionally configured to: identify transistors and associated transistor endcaps within the circuit; wherein the set of interacting geometrical features defines at least some of the transistors and associated transistor endcaps; and to generate phase shifters to be used in fabricating some of the identified transistors; wherein the layout of a given phase shifter is affected by a location of an associated endcap for the given phase shifter.
 20. The apparatus of claim 19, wherein the apparatus is further configured to determine at a parent node whether interactions between related sibling nodes cause transistor endcaps to become fieldcaps, and if so, to move geometrical features that caused the interactions to the parent node.
 21. The apparatus of claim 19, wherein the modification mechanism is additionally configured to: identify a second set of interacting geometrical features between the parent node and the set of sibling nodes; and to move the second set of interacting geometrical features from the set of sibling nodes to the parent node.
 22. The apparatus of claim 19, wherein the set of interacting geometrical features define polysilicon regions and diffusion regions on the semiconductor chip.
 23. The apparatus of claim 19, wherein the layout can define: features on the semiconductor chip; and a mask that is used to create features on the semiconductor chip.
 24. The apparatus of claim 19, wherein the design hierarchy is specified in GDSII format.
 25. A means for analyzing a layout related to a circuit on a semiconductor chip, comprising: a receiving means for receiving a design hierarchy specifying the layout of the circuit, including a set of hierarchically-organized nodes; wherein a given node in the design hierarchy specifies a geometrical feature that is comprised of lower-level geometrical features that are represented by lower-level nodes located under the given node in the design hierarchy; a modification means for modifying the design hierarchy to produce a modified design hierarchy; wherein the modification means includes, an examination means for examining a set of sibling nodes that are located under a parent node in the design hierarchy, an identification means for identifying a set of interacting geometrical features between the set of sibling nodes, and to a moving means for moving the set of interacting geometrical features from the sibling nodes to the parent node, so that the interaction is visible at the parent node, wherein other geometrical features that do not interact remain at the sibling nodes and are not moved to the parent node; and an analysis means for performing an analysis on the modified design hierarchy; wherein performing the analysis involves analyzing the set of interacting geometrical features at the parent node. 